KODAI MATHEMATICAL SEMINAR REPORTS
Online ISSN : 1881-5480
Print ISSN : 0023-2599
ISSN-L : 0023-2599
Greatest regular images of tensor products of commutative semigroups
Tom HeadNobuaki Kuroki
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JOURNAL FREE ACCESS

1975 Volume 26 Issue 2-3 Pages 132-136

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Abstract
Let A be a commutative semigroup which has either a greatest regular image or a greatest group image. Then for any commutative semigroup B, AB has a greatest image of the same type and it is describable by standard constructions based on A and B. If a commutative semigroup A has a greatest group-with-zero image then AB has such an image if and only if B is archi-medean, in which case this image is again describable by standard constructions based on A and B. A handy elementary tool is the fact that the Grothendieck group of a commutative semigroup A may be regarded as the direct limit of the directed system of groups provided by ZA where Z is the additive group of integers.
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© Department of Mathematics, Tokyo Institute of Technology
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